enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_inequality

    The bounds these inequalities give on a finite sample are less tight than those the Chebyshev inequality gives for a distribution. To illustrate this let the sample size N = 100 and let k = 3. Chebyshev's inequality states that at most approximately 11.11% of the distribution will lie at least three standard deviations away from the mean.

  3. Multidimensional Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_Chebyshev...

    In probability theory, the multidimensional Chebyshev's inequality [1] is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.

  4. Law of large numbers - Wikipedia

    en.wikipedia.org/wiki/Law_of_large_numbers

    This theorem makes rigorous the intuitive notion of probability as the expected long-run relative frequency of an event's occurrence. It is a special case of any of several more general laws of large numbers in probability theory. Chebyshev's inequality. Let X be a random variable with finite expected value μ and finite non-zero variance σ 2.

  5. Chebyshev's sum inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_sum_inequality

    In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...

  6. 68–95–99.7 rule - Wikipedia

    en.wikipedia.org/wiki/68–95–99.7_rule

    A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality ...

  7. Concentration inequality - Wikipedia

    en.wikipedia.org/wiki/Concentration_inequality

    Chebyshev's inequality can be seen as a special case of the generalized Markov's inequality ... is the probability that a single random variable is ...

  8. Irénée-Jules Bienaymé - Wikipedia

    en.wikipedia.org/wiki/Irénée-Jules_Bienaymé

    He contributed to the fields of probability and statistics, and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé–Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.

  9. Coupon collector's problem - Wikipedia

    en.wikipedia.org/wiki/Coupon_collector's_problem

    In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...